# How To Find The Median And Variance?

• March 21st 2010, 03:48 PM
AlphaRock
How To Find The Median And Variance?
Can somebody show me how to find the median and variance of this piece wise function? I've been trying so hard to do it.

f(x) =
4/(x^5) , x >= 1
0, otherwise

Ans: 1.11, 7/9
• March 21st 2010, 05:18 PM
Moo
Hello,

Compute the cdf :

F(t)=0 if t<1
$F(t)=\int_{1}^t 4x^{-5}~dx=1-\frac{1}{t^4}$ if t>1

The median is the value m such that $F(m)=0.5$. Shouldn't be too difficult...

The variance is $E[X^2]-E[X]^2=\int_1^\infty x^2f(x) ~dx-\left(\int_1^\infty xf(x) ~dx\right)^2=\dots$

Note : the fact that it is piecewise is not that important. Here, it just tells you the range of the distribution.